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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: For today's FOTD we take a trip to the barnyard to see the "Chicken Scratches" in the dirt there. Well, what else could I name such a scratchy image? The expression behind the scratchiness combines various portions of Z, (1/Z), Z^2, and Z^2.1. The whole works is iterated by the MandelbrotMix3a formula, which works like the MandelbrotMix4 formula, except that it combines 4 different powers of Z instead of 2, and the critical points must be calculated somehow by the user and entered as real(p5). I use the graphical method of calculation. The parent fractal appears as an oversized M-set rotated 180 degrees, so that east is west. This figure is quite normal appearing in its overall shape, but in its filaments, craziness appears. The filaments start out from their buds in a normal enough manner, but halfway to their ends, they split in two. This splitting is most obvious in the period-2 filament, which starts out pointing directly east along the positive X-axis, but before it reaches the large midget, splits in two. Today's image is located near the point where the splitting takes place. The -0.25*(Z^2.1) part of today's formula is the main driving force behind the image. The main feature of the image is the 'scratches' that surround the midget. Such scratches are a common feature along the 'main stem' area of Mandeloids of orders such as 2.1. When coloring the image, I added the purplish aura around the midget to intentionally give the whole image a kind of coronal discharge effect. The rest of the colors were intensified in a separate program. The intensification is included in the attached parameter file, which runs in 3-1/2 minutes on my tired machine, faster on newer models. Another way to see the chicken scratches is to download the finished image from one of the FOTD web sites at: Saturday was sunny and hot here at Fractal Central. Luckily for the cat duo the rain bypassed this area, giving them a lazy afternoon in the yard. The temperature of 93F 34C insured that their afternoon would be lazy. Today is starting in a similar manner. If the rain stays away, the duo will have another pleasant day. As for me, I'm ready to pass the day doing as little real work as possible. Until next fractal, take care, and see you in 24 hours. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Chicken_Scratches { ; time=0:03:30.64--SF5 on a p200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix3a function=ident passes=1
center-mag=+16.3204451061389/-0.011735917608758/44\
979.7/1/137.5/-3.38639630226289512e-010 params=1/1\
/-1/-1/0.25/2/-0.25/2.1/7.26855686921/3500 float=y
maxiter=300 inside=0 logmap=34 periodicity=10
colors=000000000000000000000000000400A0OG0SL4XRAaV\
Jh_NodPtjRzNd0Zq0sz0zv0us4boGRkP2gZ4di8`s8XzHZzNZz\
X`xb`xi`xsbvzbvzduzduzduz`vzXvzTvsPvkLvdHxXExPAxH6\
xA2xC0xE0sG0mH0iJ2dL2ZN2VP2PR4JT4GV4AX46Z80`A0bC0d\
E0eG0g00i00k00m00o20q80sE0uH0vN0xT0zZ0zd0zi0zm0ze2\
zZ4zR6zJ8zCAz4Cz0Ez0Gz0Hz0Hz0Gz0Ez2EzCCzLCzVAzdAzm\
8zv8zz6zz6zz8zzAzxCzuEzoEziGzdHz`JzVLzPLzJNzGPzARz\
4Tz0TzARzHPzRPzZNzgNzoLzvLzzGzzAzzCzzCzzEzzEzzEzzC\
zzAzz8zz6zz4zz2zz0zz0zz0zz0zz0zz0zz2zzCzzJzzTzz`zz\
izzqzzszzuzzuzzvzzvzzxzzxzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzxzzvzzuzzszzqzzozzmzzkzzizzgzzezzezzmzzv\
zzzzzzzzzzzzzzvzzszzmzzizzdzz`zzVzzRzzLzzHzzCzz8zz\
AzzAzzCzzCzzCzzEzzEzzGzzGzzGzzCzzAzz8zz4zz2zz0zz0z\
z0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz4zzG\
zzPzz`zzizzuzzzzzzzzzzzzzzszzmzzezz`zzTzzNzzGzzAzz\
EzzGzzJzzLzzPzz8zz6zz4zz2 }
frm:MandelbrotMix3a {; Jim Muth
z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1),
d=real(p2), f=imag(p2), g=real(p3), h=imag(p3),
j=real(p4), k=imag(p4), l=imag(p5)+100:
z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c,
|z| <=l }
END 20.0 PAR-FORMULA FILE==================================
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times.
